Details

sample124.0ms

Algorithm

intervals

Results

100.0ms

620×

body

valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
4	2051
3	638
2	183
1	56
0	18

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
0.1b	(* (* a a) (- 1 a))
0.3b	(* (* b b) (+ 3 a))
0.3b	(pow (+ (* a a) (* b b)) 2)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-r`
8×	`fma-def`
6×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `difference-of-squares` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 121

Calls

4 calls:

69.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
25.0ms	(* (* a a) (- 1 a))
26.0ms	(* (* b b) (+ 3 a))
9.0ms	(pow (+ (* a a) (* b b)) 2)

series334.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
71.0ms	(* (* a a) (- 1 a))
45.0ms	(* (* b b) (+ 3 a))
54.0ms	(pow (+ (* a a) (* b b)) 2)

simplify1.1s

Counts

133 → 133

Iterations

Iter	Nodes
2	2206
1	677
0	229

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2)
0.3b	(pow (+ (* a a) (* b b)) 2)
8.6b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
8.6b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`pow-unpow` `unpow-prod-down` `add-exp-log` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

16.0ms	(pow (+ (* a a) (* b b)) 2)
16.0ms	(pow (+ (* a a) (* b b)) 2)
66.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
105.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (+ (* a a) (* b b)) 2)
49.0ms	(pow (+ (* a a) (* b b)) 2)
250.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
250.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

simplify2.1s

Counts

90 → 90

Iterations

Iter	Nodes
3	4360
2	857
1	262
0	107

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a a) (- 1 a))
0.2b	(* (* a a) (* a a))
0.3b	(* (* b b) (+ 3 a))
0.8b	(* (* b b) (+ (* b b) (* (* a a) 2)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

130×	`pow1`
36×	`pow-prod-up`
32×	`pow-prod-down`
31×	`add-cbrt-cube` `add-exp-log`
25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`pow-sqr`
19×	`add-cube-cbrt`
18×	`pow-plus` `prod-diff`
17×	`prod-exp` `cbrt-unprod`
14×	`associate-r`
13×	`pow2` `distribute-rgt-in` `distribute-lft-in`
6×	`associate-*r/`
4×	`expm1-log1p-u` `associate-l` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`sub-neg` `flip3-+` `flip-+` `difference-of-squares`
1×	`flip3--` `swap-sqr` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

26.0ms	(* (* a a) (- 1 a))
24.0ms	(* (* a a) (* a a))
22.0ms	(* (* b b) (+ 3 a))
32.0ms	(* (* b b) (+ (* b b) (* (* a a) 2)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* a a) (- 1 a))
42.0ms	(* (* a a) (* a a))
46.0ms	(* (* b b) (+ 3 a))
64.0ms	(* (* b b) (+ (* b b) (* (* a a) 2)))

simplify998.0ms

Counts

180 → 180

Iterations

Iter	Nodes
2	2302
1	690
0	231

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* (* b b) (+ (* b b) (* (* a a) 2))) (pow a 4)) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
0.1b	(* (* a a) (- 1 a))
0.3b	(* (* b b) (+ 3 a))
0.8b	(* (* b b) (+ (* b b) (* (* a a) 2)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-*r/`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
20×	`frac-add` `add-cube-cbrt`
19×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`prod-diff`
15×	`flip3-+` `flip-+`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-r`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `fma-def` `associate-l` `*-commutative` `unswap-sqr`
2×	`associate-+r+` `sub-neg` `difference-of-squares`
1×	`+-commutative` `associate-+l+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 135

Calls

4 calls:

201.0ms	(+ (+ (* (* b b) (+ (* b b) (* (* a a) 2))) (pow a 4)) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
29.0ms	(* (* a a) (- 1 a))
32.0ms	(* (* b b) (+ 3 a))
28.0ms	(* (* b b) (+ (* b b) (* (* a a) 2)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (+ (* (* b b) (+ (* b b) (* (* a a) 2))) (pow a 4)) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
60.0ms	(* (* a a) (- 1 a))
36.0ms	(* (* b b) (+ 3 a))
82.0ms	(* (* b b) (+ (* b b) (* (* a a) 2)))

simplify2.4s

Counts

147 → 147

Iterations

Iter	Nodes
2	5156
1	1162
0	336

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes284.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	35
1	35
0	22

end0.0ms

sample3.9s

Algorithm

intervals

Results

3.5s

20611×

body

valid